Saturable absorption (SA) is an extreme nonlinear phenomenon that consists of the quenching of optical absorption under high-intensity illumination. This effect, which is an inherent property of photonic materials, constitutes a key element for passive mode-locking (PML) in laser cavities, where continuous waves are broken into a train of ultrashort optical pulses. Most materials undergo SA at very high optical intensities, in close proximity to their optical damage threshold. Currently, state-of-the-art semiconductor-based SA mirrors are routinely employed for PML lasers. However, these mirrors operate in a narrow spectral range, are poorly tunable, and require advanced fabrication techniques. Recently, carbon nanomaterials have emerged as an attractive, viable, and cost-effective alternative for the development of next-generation PML lasers. For example, carbon nanotubes undergo SA at rather modest light intensities, while their operation wavelength (determined by the energy band gap) can be manipulated by tuning their diameter. Broadband operation has been demonstrated by using an ensemble of CNTs with a wide distribution in diameter, at the expense of higher linear loss from off-resonance tubes. Graphene overcomes this limitation thanks to its peculiar conical band structure, which gives rise to broadband resonant SA at remarkably low light intensity that can further be tuned by means of an externally applied gate voltage. Graphene-based SA components have been used to achieve PML ultrafast laser operation, broadband tunability, and quality-factor switching. Graphene multilayers have also been employed to generate large energy pulses and to achieve PML in fiber lasers with normal dispersion. In addition, recent theoretical investigations predict single-mode operation of random lasers by embedding graphene flakes in a gain medium.
Here we calculate intraband and interband contributions to SA of extended graphene by nonperturbatively and semianalytically solving the single-particle Dirac equation for massless Dirac fermions (MDFs) in the presence of an external electromagnetic field retaining only one-photon processes. We further investigate the dependence of the intensity-saturated grapheme conductivity on doping, temperature, and optical frequency. Interestingly, we find a remarkably low intensity threshold for SA, which is consistent with available experimental reports. Our calculations indicate a strong quenching of absorption depth produced by electrical doping (which can be controlled through gating), as well as a weak dependence on electron temperature. Additionally, through time-domain simulations based on an atomistic tight-binding/single-particle density-matrix formalism, we study SA in graphene nanoribbons, including finite-size effects and electron-electron interactions that play a significant role in the optical response of nanostructured graphene. Surprisingly, we find that while the linear absorption predicted in atomistic simulations is reduced compared to that of extended graphene, its nonlinear saturation intensity threshold is in good quantitative agreement with predictions based on the MDF model. Deviations from the semianalytical treatment occur only at high doping, where SA is quenched and multiphoton processes lead to an intensity-dependent increase of absorption. We anticipate that the present findings will impact the future development of graphene-based PML fibre lasers and single-mode random lasers.
High-harmonic generation (HHG) in condensed-matter systems is both a source of fundamental insight into quantum electron motion and a promising candidate to realize compact ultraviolet and ultrafast light sources [1-3]. Here we argue that the large light intensity required for this phenomenon to occur can be reached by exploiting localized plasmons in conducting nanostructures. In particular, we demonstrate that doped graphene nanostructures combine a strong plasmonic near-field enhancement and a pronounced intrinsic nonlinearity that result in efficient broadband HHG within a single material platform . We extract this conclusion from time-domain simulations using two complementary nonperturbative approaches based on atomistic one-electron density matrix and massless Dirac-fermion Bloch-equation pictures, where the latter treatment is supplemented by a classical electromagnetic description of the self-consistent field produced by the illuminated nanostructure. High harmonics are predicted to be emitted with unprecedentedly large intensity by tuning the incident light to the localized plasmons of ribbons and finite islands. In contrast to atomic systems, we observe no cutoff in harmonic order, while a comparison of the predicted HHG from graphene to that observed in solid-state systems suggests that the HHG yields measured in semiconductors can be produced by graphene plasmons using 3-4 orders of magnitude lower pulse fluence. Our results support the strong potential of nanostructured graphene as a robust, electrically-tunable platform for HHG.
 S. Ghimire et al., “Observation of High-Order Harmonic Generation in a Bulk Crystal,” Nat. Phys. 7, 138 (2011).
 O. Schubert et al., “Sub-Cycle Control of Terahertz High-Harmonic Generation by Dynamical Bloch Oscillations,” Nat. Photon. 8, 119 (2014).
 T. T. Luu et al., “Extreme Ultraviolet High-Harmonic Spectroscopy of Solids,” Nature 521, 498 (2015).
 J. D. Cox, A. Marini, and F. J. García de Abajo, “Plasmon-Assisted High-Harmonic Generation in Graphene,” Nat. Commun. 8, 14380 (2017).
The realization of efficient high-harmonic generation (HHG) in solid-state systems is anticipated to pave the way for compact ultraviolet and ultrafast light sources, and to provide fundamental insight into quantum many-body electron motion [1-3]. Here we argue that the large light intensity required for HHG to occur can be reached by exploiting localized plasmons in doped graphene nanostructures. In particular, we demonstrate that the synergistic combination of strong plasmonic near-field enhancement and a large intrinsic nonlinearity originating from the anharmonic charge-carrier dispersion of graphene result in efficient broadband high-harmonic generation within a single material . We extract this conclusion from rigorous time-domain simulations using complementary nonperturbative approaches based on atomistic one-electron density matrix and massless Dirac-fermion Bloch-equation pictures, where the latter treatment is supplemented by a classical electromagnetic description of the plasmonic near-field enhancement produced by the illuminated nanostructure.
High harmonics are predicted to be emitted with unprecedentedly large intensity by tuning the incident light to the localized plasmon resonances of ribbons and finite islands, which in turn can be actively modulated via electrical gating. In contrast to HHG in atomic systems, we observe no cutoff in harmonic order, while a comparison of graphene plasmon-assisted HHG to recent measurements in solid-state systems suggests that the HHG yields from bulk semiconductors can be produced by graphene plasmons using 3-4 orders of magnitude lower pulse fluence. Our results support the strong potential of nanostructured graphene as a robust, electrically-tunable platform for HHG.
The combination of graphene’s intrinsically-high nonlinear optical response with its ability to support long-lived, electrically tunable plasmons that couple strongly with light has generated great expectations for application of the atomically-thin material to nanophotonic devices. These expectations are mainly reinforced by classical analyses performed using the response derived from extended graphene, neglecting finite-size and nonlocal effects that become important when the carbon layer is structured on the nanometer scale in actual device designs. Based on a quantum-mechanical description of graphene using tight-binding electronic states combined with the random-phase approximation, we show that finite-size effects produce large contributions that increase the nonlinear response associated with plasmons in nanostructured graphene to significantly higher levels than previously thought, particularly in the case of Kerr-type optical nonlinearities. Motivated by this finding, we discuss and compare saturable absorption in extended and nanostructured graphene, with or without plasmonic enhancement, within the context of passive mode-locking for ultrafast lasers. We also explore the possibility of high-harmonic generation in doped graphene nanoribbons and nanoislands, where illumination by an infrared pulse of moderate intensity, tuned to a plasmon resonance, is predicted to generate light at harmonics of order 13 or higher, extending over the visible and UV regimes. Our atomistic description of graphene’s nonlinear optical response reveals its complex nature in both extended and nanostructured systems, while further supporting the exceptional potential of this material for nonlinear nanophotonic devices.
Saturable absorption (SA) is an inherent property of photonic materials that manifests itself as an absorption quenching at high light intensities and is a key element for passive mode-locking (PML) in laser cavities, where continuous waves break into a train of ultrashort optical pulses. Currently, state-of-the-art semiconductor-based SA mirrors are routinely employed for PML lasers. However, these mirrors operate in a narrow spectral range, are poorly tunable, and require advanced fabrication techniques. Graphene overcomes this limitation thanks to its peculiar conical band structure, providing a universally-resonant wavelength-independent SA at low light intensity that can be further electrically tuned be means of an externally applied gate voltage. Here, we calculate intraband and interband contributions to SA of extended graphene by solving non-perturbatively the single-particle Dirac equation for massless Dirac fermions in the presence of an external electromagnetic field and comparing results with atomistic calculations in the framework of tight-binding and random-phase approximation. Further, we investigate the optical properties of randomly-oriented undoped graphene flakes embedded in externally pumped amplifying media. We demonstrate a novel mechanism leading to stable and tunable single-mode cavity-free lasing characterized by a well-determined and highly coherent spatial pattern. This cavity-free lasing mechanism profoundly relies on graphene highly-saturated absorption at rather modest light intensities, a remarkable property which enables self-organization of light into a well determined spatial mode profile.
We propose the exploitation of plasmons in graphene nanoislands as a promising platform for sensing through surface-enhanced infrared absorption and Raman scattering. Our calculations indicate that the large electrical tunability of graphene enables the identification of molecular resonances by recording broadband absorption or inelastic scattering, replacing wavelength-resolved light collection by a signal integrated over photon energy as a function of the graphene doping level. Our results pave the way for the development of novel cost-effective sensors capable of identifying spectral signatures of molecules without using spectrometers and laser sources.